There is a desire to provide a way to determine relative skills of players of games such as computer games, chess, tennis and any other suitable type of game. Our earlier Bayesian Scoring system is implemented in Xbox Live (trade mark) and is currently commercially available under the trade name TrueSkill (trade mark). Here we build on our earlier work and use a new method of computation to enable processing times to be significantly reduced. Message passing techniques are adapted to enable computation of updated skill beliefs to be obtained quickly even in the case of multiple teams of multiple players.
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1. A method comprising: determining an indication of the relative skill of at least a first player and a second player of a game based at least in part on the outcome of one or more such games involving those players via operations comprising: (i) for each player, accessing statistics describing a probability distribution associated with belief about skill of that player; (ii) receiving information about the outcome of one of the games, the information comprising, for at least one player; ordered ranking information that indicates a relative finishing order of the players according to rules of the game and indicates performance for the player; and an indication of a length of time that the at least one player participated in the one of the games, the length of time being less than a total game time of the one of the games, the statistics for the at least one player being updated on the basis of the indication, the one of the games triggering a single update of the relative skill of the plurality of players participating in the one of the games, the single update including an update of the ranking of the at least one player based on the updated statistics; and (iii) forming a factor graph comprising nodes, said graph being formed using the received information about the outcome, and instantiating at least some of the nodes with the statistics; and updating the statistics associated with each player by using message passing techniques over the factor graph such that, for each player, the probability distribution indicating the belief about the skill of the player becomes based at least in part on the outcome of the game.
A method for determining the relative skill of players in a game. It involves: (1) accessing skill statistics (probability distribution) for each player; (2) receiving game outcome information, including each player's finishing order (ranking) and their participation time (less than the total game time). The system updates player statistics based on participation time. A single update is triggered after each game and includes an update to the ranking of each participating player. (3) Constructing a factor graph using game outcome information and instantiating some nodes with player statistics. Finally, it updates each player's skill statistics using message passing techniques over the factor graph, adjusting the probability distribution based on the game outcome.
2. A method as claimed in claim 1 , wherein the statistics comprise at least a mean and a variance describing each probability distribution.
The method for determining the relative skill of players in a game, as described above, utilizes statistics that include at least the mean and variance to describe each probability distribution associated with a player's skill. This means that each player's skill is represented by a distribution characterized by its average value (mean) and spread (variance), which are updated based on game outcomes and participation.
3. A method as claimed in claim 1 , wherein the probability distributions are Gaussian.
The method for determining the relative skill of players in a game, as described above, uses Gaussian distributions to represent the probability distribution associated with each player's skill. This means that the belief about each player's skill is modeled using a normal distribution, characterized by a mean and variance that are updated based on game outcomes and participation.
4. A method as claimed in claim 1 , wherein the factor graph is acyclic.
The method for determining the relative skill of players in a game, as described above, constructs a factor graph that is acyclic. This means the graph structure used for message passing does not contain any cycles, ensuring that the message passing algorithm converges and produces stable skill updates.
5. A method as claimed in claim 1 , wherein the message passing techniques applied over the factor graph are arranged to perform Bayesian inference processes.
The method for determining the relative skill of players in a game, as described above, uses message passing techniques over the factor graph that are specifically arranged to perform Bayesian inference processes. This implies that the skill updates are performed in a statistically sound manner, incorporating prior beliefs about player skills with new evidence from game outcomes.
6. A method as claimed in claim 1 , wherein said factor graph comprises a plurality of groups of nodes, each group being associated with a particular player and comprising nodes linked in series.
The method for determining the relative skill of players in a game, as described above, forms the factor graph using a plurality of groups of nodes, where each group is associated with a particular player and comprises nodes linked in series. This creates a structured representation of each player's skill and performance within the factor graph.
7. A method as claimed in claim 6 , wherein said factor graph comprises a plurality of second groups of nodes, each second group being associated with a team of players.
The method for determining the relative skill of players in a game, as described above where the factor graph has groups of nodes linked in series for each player, includes second groups of nodes. Each second group is specifically associated with a *team* of players. This extension allows for skill determination in team-based games by aggregating individual player skills.
8. A method as claimed in claim 6 , wherein said groups of nodes are linked with edges such that the order of the linking reflects the outcome of the game.
The method for determining the relative skill of players in a game, as described above where the factor graph has groups of nodes linked in series for each player, connects these groups of nodes with edges. The order of these connections reflects the outcome of the game (e.g., winning or losing). This ensures that the factor graph structure represents the relationships between players and their relative performance.
9. A method as claimed in claim 8 , wherein said groups of nodes are also ordered in the factor graph on the basis of teams that the players are in.
The method for determining the relative skill of players in a game, as described above where the factor graph has groups of nodes linked in series for each player and the groups are linked to reflect the game outcome, further organizes these groups based on the teams the players are on. This is important in team-based games because it takes into account team membership in the skill determination process, further refining accuracy.
10. A method as claimed in claim 1 , for determining an indication of the relative skill of players from games involving three or more players.
The method described above is specifically designed for determining the relative skill of players in games involving three or more players. This extends the algorithm's applicability beyond simple two-player games to more complex scenarios with multiple participants.
11. A method as claimed in claim 1 , wherein the length of time relative to the total game time is a weighting factor for updating the statistics.
In the method for determining the relative skill of players, the length of time a player participates in a game, relative to the total game time, acts as a weighting factor when updating the player's skill statistics. This means that players who participate for a shorter time have their skill estimates adjusted less drastically than those who play for the full duration, accounting for varying levels of involvement.
12. A method as claimed in claim 1 , wherein information about the outcome of the game comprises a partial ranking of players, said partial ranking comprising order information for at least one player and no order information among a plurality of other players, and wherein said factor graph is formed such that a link is created between a node associated with said at least one player and a node associated with each of the said other players.
In the method for determining relative skill, the information about the game's outcome includes a partial ranking of players. This ranking provides order information for at least one player but lacks order information among other players. The factor graph is formed by linking the node associated with the ranked player to each node associated with the unranked players. This handles scenarios where not all players' relative positions are known.
13. An apparatus comprising: one or more processors arranged to determine an indication of the relative skill of at least a first player and a second player of a game based at least in part on the outcome of one or more such games involving those player via operations comprising: (i) an input arranged to access, for each player, statistics describing a probability distribution associated with belief about skill of that player; (ii) an input arranged to receive information about the outcome of one of the games, the information comprising, for at least one player, ordered ranking information that indicates a relative finishing order of the players according to rules of the game, and an indication of a length of time that the at least one player participated in the one of the games, the length of time being less than a total game time of the one of the games, the statistics for the at least one player being updated on the basis of the indication, the outcome of the one of the games being unknown for the at least one player until completion of the one of the games, the ranking of the at least one player being updated based on the updated statistics; and (iii) means for forming a factor graph comprising nodes, said graph being formed using the received information about the outcome, said means also being for instantiating at least some of the nodes with the statistics; and the one or more processors arranged to update the statistics associated with each player by using message passing techniques over the factor graph such that, for each player, the probability distribution indicating the belief about the skill of the player becomes based at least in part on the outcome of the game.
An apparatus (system) for determining the relative skill of players in a game. It has one or more processors that: (1) access skill statistics (probability distribution) for each player via an input; (2) receive game outcome information via an input, including each player's finishing order (ranking) and their participation time (less than the total game time). Statistics for the at least one player being updated on the basis of the indication, the outcome of the one of the games being unknown for the at least one player until completion of the one of the games, the ranking of the at least one player being updated based on the updated statistics; (3) form a factor graph using game outcome information, instantiating some nodes with player statistics. The processors update player statistics using message passing over the factor graph, adjusting the probability distribution based on the game outcome.
14. An apparatus as claimed in claim 13 , wherein the factor graph is acyclic.
The apparatus for determining the relative skill of players, as described above, uses a factor graph that is acyclic. This ensures the message-passing algorithm converges correctly.
15. An apparatus as claimed in claim 13 , wherein the message passing techniques applied over the factor graph are arranged to perform Bayesian inference processes.
The apparatus for determining the relative skill of players, as described above, uses message passing techniques over the factor graph to perform Bayesian inference. This allows for statistically sound updates to skill estimates.
16. An apparatus as claimed in claim 13 , wherein said factor graph comprises a plurality of groups of nodes, each group being associated with a particular player and comprising nodes linked in series.
The apparatus for determining the relative skill of players, as described above, uses a factor graph composed of groups of nodes. Each group corresponds to a player, and the nodes within each group are linked in series.
17. An apparatus as claimed in claim 13 , wherein said factor graph comprises a plurality of groups of nodes, each group being associated with a team of players.
The apparatus for determining the relative skill of players, as described above, utilizes a factor graph that includes groups of nodes associated with teams of players. This supports skill estimation in team-based games.
18. An apparatus as claimed in claim 16 , wherein said groups of nodes are linked with edges such that the resulting order reflects the outcome of the game.
The apparatus for determining the relative skill of players, as described above, uses a factor graph with groups of nodes for each player linked in series. These groups are linked together with edges so that the resulting order reflects the game's outcome.
19. A method comprising: receiving information about the outcome of a game, the information comprising, for at least one player, ordered ranking information that indicates a relative finishing order of one or more players according to rules of the game and indicates players' performance and an indication of a length of time that the at least one player participated in the game, the length of time being less than a total game time of the game, the game triggering a single update of skill levels of the plurality of players participating in the game, the single update including an update of the ranking of the at least one player based on the updated statistics; forming an acyclic factor graph that includes: for each of a plurality of players of the game: a factor node that accesses a Gaussian distribution that represents a skill level of the player; a player skill variable node that stores mean and variance parameters of the Gaussian distribution; a factor node that reflects player performance by modifying the variance parameter based at least in part on the outcome of the game when the game has finished; and a player performance variable node that stores the mean and the modified variance parameter; and performance difference factor nodes for calculating performance differences between consecutive players, based at least in part on the ordered indication of players' performance; and for each of the plurality of players of the game, updating the Gaussian distribution that represents the skill level of the player, the Gaussian distribution for the at least one player being updated at least partly based on the indication.
A method updates player skill levels after a game using the following steps: Receive game outcome information including player ranking (finishing order, performance) and participation time for at least one player (less than total game time). This triggers a single skill level update for all players, including an update to the at least one player's ranking based on updated statistics. Form an acyclic factor graph comprising: (1) A Gaussian distribution representing each player's skill (factor node) with a mean and variance stored in a player skill variable node. (2) A factor node to modify variance after game based on the outcome. (3) A player performance variable node to store the mean and modified variance. (4) Performance difference factor nodes to calculate performance differences between consecutive players based on their order. Update each player's skill Gaussian distribution, based on the game and their participation.
20. A method as claimed in claim 19 , wherein the acyclic factor graph further comprises: a factor node that calculates a team performance by combining values from the player performance variable nodes of each player that is a member of the team; and performance difference factor nodes for calculating performance differences between consecutive teams, based at least in part on an ordered indication of teams' performance.
The method described above, which updates player skill levels after a game, is expanded. It also includes: (1) A factor node to calculate team performance by combining player performance values. (2) Performance difference factor nodes for calculating performance differences between teams, based on the ordered team performance. This extends the system to handle team-based skill assessment.
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January 16, 2007
September 17, 2013
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